Joe Biden has defended his rhetoric against Donald Trump and cited why it was important, in his first interview since the attempt on his political rival's life.

The president said his campaign had a duty to clearly communicate the threat of a second Trump term, adding that his words were not the ones that needed to be tempered.

However, he told NBC's Lester Holt it had been a "mistake" to have said it was “time to put Trump in a bullseye" during a private donor call days before the assassination attempt on Trump at a Saturday rally in Pennsylvania.

Mr Biden said he meant Democrats needed to focus more on Trump, his policies and the false statements he made during the presidential debate late last month.

Throughout the interview, Mr Biden made it clear he would not be stepping aside in the presidential race - despite calls from members of his own party after his poor debate performance.

"I'm old," he lamented, while also noting he's only three years younger than Trump. He said his mental acuity was fine and listed his accomplishments as president - but acknowledged he was working to reaffirm to Americans that he was up the job.

"I understand why people say, 'God, he’s 81 years old. Whoa. What's he going to be when he’s 83 years old, 84 years?' It’s a legitimate question to ask," he said.

He said he put his faith in the voters who overwhelming backed him in the Democratic primary. "I listen to them."

The president has repeatedly called for Americans to "lower the temperature" since the shooting on Saturday, where Trump's ear was grazed by a bullet.

One crowd member was killed and two others were critically injured in the attack.

About a dozen Republicans have blamed Mr Biden and other Democrats for inciting the attempt on Trump's life. Many have specifically cited Mr Biden's "bullseye" comment.

JD Vance, who was announced as Trump's presidential running mate on Monday, said in the wake of the shooting that Democratic rhetoric about the Republican candidate "led directly to President Trump's attempted assassination".

According to Politico, Mr Biden had said on the donor call: "I have one job, and that's to beat Donald Trump. I'm absolutely certain I'm the best person to be able to do that. So, we're done talking about the debate. It’s time to put Trump in a bullseye."

President Biden, in an Oval Office address on Sunday, denounced the attack and called for Americans to "take a step back", warning that "political rhetoric in this country has gotten very heated".

When asked in the NBC interview if he had also taken a step back to examine his past remarks for anything "that could incite people who are not balanced", Mr Biden said the inflammatory rhetoric had not come from him.

"I've not engaged in that rhetoric," Mr Biden said. "Now, my opponent is engaged in that rhetoric."

"How do you talk about the threat to democracy, which is real, when a president says things like he says? Do you just not say anything, because it may incite somebody?

"I am not the guy that said I want to be a dictator on day one, I am not the guy that refused to accept the outcome of the election."

The FBI has identified the gunman who targeted Trump as Thomas Matthew Crooks, 20, a kitchen worker from Bethel Park, Pennsylvania, who is a registered Republican.

A Secret Service sniper shot Crooks dead after he fired at the former president.